BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.3, Problem 21E
To determine

Find the equation of the tangent line usinggiven data.

Expert Solution

Answer to Problem 21E

The equation of the tangent line is y=x+1 .

Explanation of Solution

Given:

The given curve is y=x+cosx and the given pointis (0,1) .

Calculation:

Find the derivative of the function.

  y=x+cosx

Apply sum rule.

  (f+g)'=f'+g'

  dydx=ddx(x)+ddx(cosx)

Use derivative rule ddx(xn)=nxn1 and ddx(cosx)=sinx .

  dydx=1+(sinx)dydx=1sinx

Substitute the value of x=0 in the derivative.

  dydx=1sinx=1sin(0)=10=1

Slope =1

Use point-slope form for the equation of tangent line.

  yy1=m(xx1)y1=1,x1=0,m=1y1=1(x0)y1=xy1+1=x+1y=x+1

Hence theequation of the tangent line is y=x+1 .

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